1. **Problem statement:** A company sells goods at 8000 per unit. The total cost (TC) to produce Q units is given by $$TC = 900000 + 3000Q$$. We need to find: a) The break-even point (BEP) quantity. b) Profit or loss if 200 units are sold. c) Profit or loss if 150 units are sold. 2. **Formula and rules:** - Revenue (R) = Price per unit $ \times $ Quantity = $$8000Q$$ - Profit ($\pi$) = Revenue - Total Cost = $$\pi = 8000Q - (900000 + 3000Q)$$ - Break-even point occurs when Profit = 0, i.e., Revenue = Total Cost. 3. **Step-by-step solution:** **a) Find BEP:** Set Revenue = Total Cost: $$8000Q = 900000 + 3000Q$$ Subtract $$3000Q$$ from both sides: $$8000Q - 3000Q = 900000$$ $$5000Q = 900000$$ Divide both sides by 5000: $$Q = \frac{900000}{5000} = 180$$ So, the break-even quantity is 180 units. **b) Profit or loss at 200 units:** Calculate total revenue: $$R = 8000 \times 200 = 1600000$$ Calculate total cost: $$TC = 900000 + 3000 \times 200 = 900000 + 600000 = 1500000$$ Calculate profit: $$\pi = R - TC = 1600000 - 1500000 = 100000$$ Since profit is positive, the company makes a profit of 100000. **c) Profit or loss at 150 units:** Calculate total revenue: $$R = 8000 \times 150 = 1200000$$ Calculate total cost: $$TC = 900000 + 3000 \times 150 = 900000 + 450000 = 1350000$$ Calculate profit: $$\pi = R - TC = 1200000 - 1350000 = -150000$$ Since profit is negative, the company incurs a loss of 150000.